Properties

Label 2.199.abz_bof
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $1 - 51 x + 1045 x^{2} - 10149 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0810958877955$, $\pm0.182598387842$
Angle rank:  $2$ (numerical)
Number field:  4.0.222573.1
Galois group:  $D_{4}$
Jacobians:  24

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30447 1548138609 62078532588333 2459391344344332477 97393911071387418585072 3856887910875964035545473689 152736585108343699658251911049521 6048521418500753063905590357221750133 239527496523770704767162137692625015341131 9485528389642825595779865469601544416420349184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 149 39091 7877387 1568250139 312080349884 62103854990095 12358664468771189 2459374193351624035 489415464129052796951 97393677359679137558686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.222573.1.
All geometric endomorphisms are defined over $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.bz_bof$2$(not in LMFDB)